Archive for category Physics

One thing The Mail normally does quite well are giant picture spreads – stories with lots of giant photos and maybe a couple of hundred words of text to explain them. Normally…

Am I being pedantic? I don’t care; the “spiralling meteors” are not meteors, they’re stars! As the Earth turns, the stars seem to rotate around the Pole Star (the “stationary” speck of light in the centre of the image), and if you take a long exposure photograph of them they seem to draw circles in the sky. Now, there are meteors in this image but they are not spiralling and they are, err, a bit tricky to see, especially since The Mail has squished the images down to web resolution.

Edit: After I’ve complained about the Mail squashing the image too much, WordPress has gone and squashed it even further. Click on the images to view them unsquashed.

Can you see them? They’re more visible in the full size version, and they do not spiral. In fact, that’s how you tell a meteor from a star – the meteor moves so quickly that the rotation of the Earth has no effect on its apparent path, so it blazes in a straight line across the sky. All in all, this is a great star trail picture, but it’s not the best meteor picture ever, and the way The Mail has presented it means it’s not a meteor picture at all.

The bright moon made watching/capturing difficult this year and the very wide angle shot makes for a good composition but lesser meteor detail.

Incidentally, there are a lot of really good photos on Humpage’s website – not just of stars and satellites, but hurricanes, icebergs and aurorae too – and, unlike The Mail, he knows the difference between a star and a meteor. Enjoy!

Neptune’s birthday is today, not tomorrow! We’ll all be celebrating on the wrong day!

Never mind phone hacking, this is the realscandal.

Edit: The BBC is even more wrong, claiming Neptune’s birthday is July 12. The philistines!

Double edit: In fact, it looks like we’re all right! July 10 is one average Neptunian year after the date of discovery, July 11 is the day when Neptune will have made precisely one orbit around the solar system’s barycentre (i.e., its centre of mass when you take the Sun and all the planets into account), and July 12 is the day that Neptune will have made precisely one orbit around the Sun. (A figure of July 13 is floating around as well, most likely as a result of an Indian newspaper article which has taken timezones into account). Thanks to Up, Blogstronomy and the Wikipedia users on Talk:Neptune!

British government officials approached nuclear companies to draw up a co-ordinated public relations strategy to play down the Fukushima nuclear accident just two days after the earthquake and tsunami in Japan and before the extent of the radiation leak was known.

Internal emails seen by the Guardian show how the business and energy departments worked closely behind the scenes with the multinational companies EDF Energy, Areva and Westinghouse to try to ensure the accident did not derail their plans for a new generation of nuclear stations in the UK.

I’m not sure “play down” is really the right phrase to use here. After all, this appears to be the relevant part of the worst email:

We need to quash any stories trying to compare this to Chernobyl – by using the facts to discredit.

Is that “playing down” Fukushima, or putting it in perspective? This email was sent long before the worst of the damage was known, at which point Chernobyl comparisons would have been gross exaggerations.

Yet over and over again, the Guardian seems to forget that this was written when there was little information available, and the reactors still appeared to be intact:

The business department emailed the nuclear firms and their representative body, the Nuclear Industry Association (NIA), on 13 March, two days after the disaster knocked out nuclear plants and their backup safety systems at Fukushima. The department argued it was not as bad as the “dramatic” TV pictures made it look, even though the consequences of the accident were still unfolding and two major explosions at reactors on the site were yet to happen.

Well yes, there were serious explosions that resulted in radiation release, but they hadn’t happened when the email was sent. What was the civil servant* supposed to write?

The nuclear industry, like any industry that tries to balance profit against public good (see: transport, healthcare, media, communications), is often pretty hard to defend, but to be honest, it doesn’t come across too badly in the emails.

Sometimes they seem a bit dickishly entitled – Westinghouse probably didn’t win any points for emailing the government to object to Nick Clegg’s choice of wording in a speech – but most of the time, no matter how The Guardian spins it, it’s hard to see PR collusion in EDF offering to be “sensitive” to events in Japan in decommissioning old plants, the government explaining its new build policy, or Westinghouse discussing changes in reactor design to improve earthquake safety. I certainly can’t see what’s wrong with organising a conference to discuss how to “maintain confidence among the British public on the safety of nuclear power stations” with “factual and scientific evidence”.

In fact, given that nuclear new build is a government policy being carried out by private companies, it’s hard to see how the government could have made any statements about British nuclear power without talking to the nuclear industry.

A few emails discuss the PR response, but apart from the one from the unnamed civil servant, who fair enough does seem a bit too gung-ho about nuclear power, they make it clear that the government’s position is distinct from the industry’s, and refuse to join the industry in making a joint response (for instance, check out the email “Re: Nuclear Lines – Messaging” on page 15, sent March 14, 10:31, and any other email in that converstaion).

If a reservoir had collapsed, and the government emailed water companies for comment and to discuss preventing public panic, would that be news? Probably not.

If a train had crashed, and the government invited representatives of train operators to discuss the impact on the future of the railways, would that be news? Probably not.

So when the government discusses the future of the nuclear industry with the nuclear industry following a nuclear disaster, why is that news?

* Incidentally, the civil servant’s name has been redacted, but according to the BIS, it’s someone pretty minor, not a minister or someone with power over policy. So that’s not really a “government plan” then, is it?

Like this:

The Daily Mail today has a piece about the proposed alternative to the number pi, tau (τ), equal to 2 x π.*

Basically, the reason we might want to change to tau is simple:

Pi is defined as the circumference of a circle divided by its diameter. We came up with this definition thousands of years ago, before modern geometry had taken off, and it’s a perfectly good number.

However, we now know that the diameter of a circle – the distance all the way across – isn’t really the best way to measure a circle. Instead, it’s better to measure the distance the radius of the circle – the distance from the centre to the edge. For example, if you’re working out a planet’s orbit, the distance from the planet to the Sun (radius) is a nice logical thing to measure, but the distance from the planet to the other side (diameter) of its orbit doesn’t really mean anything important.

Since the radius is half the diameter, circumference divided by radius is twice as big as circumference divided by diameter, which is why tau is twice as big as pi.

The definition of 1 radian. The red line (radius) and blue line (arc length) are the same length. By Stannered, CC-SA-BY-3.0

Tau is also nice because it makes working with angles a bit easier. The most natural way of measuring angles – the way you have to do it if you’re doing maths or physics – is to measure them in radians. The radian is defined in terms of the circle’s radius – one radian is the angle you get if you walk around the circle for a distance of one radius. If you travel 2π radians, you travel a distance which is 2 times pi times the radius, or pi times the diameter; in other words, you travel the length of a full circle, 360°.

However, that 2 in there is a bit of a pain. It basically means that, in physics or maths, whenever you’re dealing with a circle or a wave you get annoying factors of 2 popping up in your equations, and unless you’re very careful, it’s easy to forget a factor here or put an extra one in there, making your sums completely wrong. For example, to switch between ordinary frequency and angular frequency (effectively, switching from revolutions per second to radians per second), you multiply the frequency by 2π. This is a change we need to make a lot when working with waves, and it’s so easy to lose a factor of 2 when you’re working with a bulky equation.

That factor of 2 is only in there in the first place because we made the mistake of basing pi on the diameter instead of the radius. If we replaced pi with tau, 1 circle would be τ radians, and that factor of two would disappear. It wouldn’t be a groundbreaking change, but it would still be quite nice, and it would make the mathematics of circles a bit easier to understand. Of course, the hassle of teaching people to use tau instead of pi is probably greater than the benefits, so its unlikely we’ll ever give up pi.

Unfortunately, the Mail is quoting from a (paywalled) interview in The Times with University of Leeds lecturer Kevin Houston, whose and they seem to cut down what he’s said to just:

‘Mathematicians don’t measure angles in degrees, we measure them in radians, and there are 2pi radians in a circle,’ Dr Houston said.

“That leads to all sorts of unnecessary confusion. If you take a quarter of a circle, it has a quarter of 2pi radians, or half pi. For the number of radians in three quarters of a circle, you have to think about it. It doesn’t come naturally.

‘How much simpler it would be if we just used tau instead of pi,’ Dr Houston added. ‘The circle would have tau radians, a semicircle would have half tau, a quarter of a circle a quarter tau, and so on. You don’t have to think.’

Trimmed like that, it sounds like Houston is only promoting tau because he’s too stupid to work out three quarters of two (his Youtube video, linked by the Mail, explaining the mathematics of tau, shows this is not the case). So perhaps naturally, Daily Mail commenters have leapt at the chance to prove that they’re smarter than a mathematician, because really, what do mathematicians know about mathematics?!

If an ‘A’ level Maths student has trouble with the difference between Tau and Pi, then they should be on another course. Any excuse to dumb down the kids and stop them thinking for themselves!

Alan, Frankfurt, Germany (ex pat)

Right on! How dare we dumb maths down by making it slightly clearer!

‘The circle would have tau radians, a semicircle would have half tau, a quarter of a circle a quarter tau, and so on. You dont have to think.’ …..It may be appropriate for DM readers who like not to think, but I’m afraid mathematicians do think, and aren’t interested in tau, thank you very much.

This tau thing is clearly aimed at mindless rote learners but to those of us who actually understand maths, pi expresses something meaningful which is precisely why we refer to it so much.

Vincent, Glasgow

Pi and tau express more or less the exact same thing – the shape of a circle – tau just expresses it in a slightly more logical way.

As a retired Maths teacher this idea lacks intuitive sense. The whole point of the exercise is to relate the circumference of a circle to its diameter – and the ratio is the irrational number 3.14159… The ratio is NOT 6.whatever! That’s the basic theory. Then there are various formulae needed at basic school level: for example, the area of a circle is pi time radious squared. The new formula would be tau times radius squared divided by four: an extra calculation step. Or the volume of a cone pi r squared h…. and so on. And in times of austerity how many schools could afford a new set of textbooks filled with tau? (And all authored by Leeds people, no doubt!) And then there are the millions of calculators with the pi button built in…. No! This idea is like trying to say that from 2012 we’ll all drive on the right – indeed the idea of tau is worse than that because there are regions of the world already driving on the right….. This is a big UM and No No

Andrew, Cwmbran

No, but the ratio of the circumference of a circle to its radius IS 6.whatever (6.28318… in fact). The fact that the area of the circle becomes a half times tau r squared (0.5 τr2 – there’s no dividing by four involved) is one of the downsides to tau, but as Kevin explains in the video, there is a deeper mathematical reason why we would expect that half to be there, so while it’s annoying it does make sense.

This is the way you can waste a lot of time while avoiding doing anything of real interest or value to anyone. What a waste of brain cells!! Is this supported by public funds? There are real problems in the world today that are worthy of serious consideration, but when academics waste their time on things like this, they prove that they have no value to society at large and should be dismissed.

Samuel, Dubuque, Iowa

One mathematician making a 5 minute Youtube video in his spare time? How dare he! He should devote every second of his life to curing cancer!

Big Wow… Is “2pi” the only mathematical innovation Leeds University can come up with, it’s best 21st Century contribution to the advancement of mathematics? Talented Maths kids doing their 5 science A levels must be crossing Leeds off as even a 5th choice.

Russ H, Bucks

Again, this is one guy working in his spare time. This is not the only thing the University of Leeds Maths department does! (Incidentally, 55% of Leeds pure maths research is “world leading” or “internationally excellent”, and a further 40% is “internationally recognised”.)

BUT….e^([pi]i)]=-1 and this does not work for tau. There are uses for Pi beyond circles!

Miles, Australia

(This refers to Euler’s identity, eπi = -1, which gives us a nice way of representing imaginary numbers using angles. And despite what Miles says, it’s all about circles.)

That’s true, it doesn’t. Instead, eτi = 1. This is even better than Euler’s original version, since we no longer have that minus sign (and all that minus sign told us is that pi radians = half a circle, something we already know). Quite a few comments are like this – “OH NO EULER’S FORMULA IS BEAUTIFUL, WE CAN’T CHANGE PI COS THAT WILL BREAK IT” – and yet no-one actually bothers working out what it would look like with tau.

Professional jealousy. Eienstein acceepted Pi and I can assure you he was more intelligent than this egghead. This man just wants to make a name for himself. Change all the books indeed. He is “daft” !

Ruckus, myrtle Beach SC (ex pat)

And why do we bother speaking English? If German was good enough for Einstein, it’s good enough for us!

All those comments have been upvoted, by the way, unlike this comment, which currently has a score of -1:

I am in full favour of this proposition. Unfortunately, a large number of these comments seem be be from people with only a basic understanding of mathematics. Using Tau in place of Pi would reduce the need for a constant in a plethora of standard calculations involving circles and spheres, the like of which children will be schooled in. Furthermore, the simplicity of the equations using Tau may increase understanding and encourage children to pursue an interest into further mathematics. From my experience of mathematics lessons, the majority of students didn’t dislike mathematics, but rather found it too complicated to enjoy. Once provided with a topic they were able to grasp, students began to enjoy working the problems. Once children have achieved a satisfactory grasp of simple circle equations, the transition to understanding the calculus is a much easier one. I think that should the readers have been taught using Tau the comments here would be better informed.

Pep, Manchester

Good old Daily Mail comments, eh?

* They claim the idea was invented by Kevin Houston at the University of Leeds. In fact, it’s much older than that – Bob Palais first came up with it in 2001 – and Houston is just promoting it. Also, as a conflict of interest thing, I guess I should point out that Kevin taught me a few years ago, and is a thoroughly nice guy.

This will be all over the papers today, so here’s a quick run down of what’s actually happened.

Last year the World Health Organisation released its Interphone report (PDF) into the link between brain cancer and mobile phones. For the most part, they found “no increase in risk of glioma or meningioma [types of brain cancer] was observed with use of mobile phones”. However, for very heavy users (the top 10% of the population), there was a statistically significant increase in the odds of developing a form of brain cancer known as glioma but “but biases and error prevent a causal interpretation” – there is too much uncertainty in the data to know whether heavy mobile phone use caused cancer or whether something else was to blame. On the one hand, they found there appeared to be a connection between which side of the brain the tumour developed in and which hand users held the phone in – a sign that phones might cause cancer – but on the other hand, while extreme users experienced a big increase in brain tumours, people who used their phones even slightly less saw no change in brain cancer – a sign that mobile phones might not cause cancer.

Fast forward a year, and the WHO’s International Agency for Research on Cancer (IARC) has issued a press release (PDF) about an upcoming report which, based on the Interphone study and some other papers, will classify the electromagnetic (EM) fields from mobile phones as “possibly carcinogenic to humans” meaning there is “limited evidence” that they may cause cancer. In other words, it’s the exact same conclusion as the Interphone report, but this time the report is focusing on the negative – heavy doses may cause cancer – rather than the positive – light doses probably don’t cause cancer.

That in itself is very reasonable – even if mobile phones carry a very slight cancer risk, the IARC still need to know what that risk is. The problem comes when the media, reporting this in the usual shades of black and white, ignore all this nuance in favour of scares:

The Express goes for the similar “Shock cancer warning over mobile phone use“, claiming “MOBILE phones have been officially linked to cancer for the very first time by a team of world experts”. Again, the report is a year old, it’s not a shock! They also manage to get in some ridiculous guilt-by-association:

But they classified mobile phones in the same danger category as the pesticide DDT and petrol engine exhaust, meaning they are possibly carcinogenic to humans.

Petrol exhaust and DDT are pretty dangerous, but that’s not necessarily because they cause cancer! Nor does being in the same group as these mean it carries the same risk of cancer, either. It just means that we have the same level of evidence for a cancer risk, which isn’t the same thing. For example, DDT is now banned worldwide, with most developed countries banning it in the 70s. This means that people aren’t being exposed to it any more (a good thing, of course!), so we can’t study its effects and work out exactly how dangerous it is.

The Guardian meanwhile goes for a tenuous connection to the risks of mobile phone base stations and wi-fi, even though the exposure to EM from these is much lower than from holding a phone to your ear – and we know even then it’s only the heaviest exposures that may cause cancer.

The Telegraph also makes the ridiculous DDT comparison, but at least they quote the great Ed Yong, head of health information at Cancer Research UK, who sensibly sums up the evidence:

“The risk of brain cancer is similar in people who use mobile phones compared to those who don’t, and rates of this cancer have not gone up in recent years despite a dramatic rise in phone use during the 1980s.

“However, not enough is known to totally rule out a risk, and there has been very little research on the long-term effects of using phones.”

(They also quote a professor of Medical Physics and Director of the Mobile Operators Association, but to be honest, they seem to have gone into damage control mode before there’s been any damage to control. Pro-tip, guys – if you ever end a paragraph about the health risks of something by saying “The social and technological benefits also need to be emphasised“, then you sound like a cyberpunk bad guy, even if you truly mean it.)

Anyway, for a little perspective, there’s a great interview with Ed Yong about the news here. Read it!

You refuse to buy the normal energy saving compact fluorescent light (CFL) bulb, which you can get for about £1, for some reason.

You decide to buy the first of a new sort of light bulb – the LED light bulb – and in particular, you buy the smallest and brightest bulb available, which costs about $45 (£27) at the moment, and you buy it right away instead of waiting for the price to come down.

Better headline: One particular light bulb might cost $45 EACH at first (but you won’t have to buy them even if you’re American because they’re stupidly powerful and there are cheaper bulbs available which are just as bright)

Like this:

Edit: After a quick email conversation with the author, the article has now been rewritten (direct link). Although it still has a slightly cringeworthy headline, it no longer contains misunderstandings about the paper and is all in all pretty good! I’ve hidden the original post behind the cut.